It is definitely a hardware issue then. You can however try connecting it to itunes and restore the phone from there. It will download the new software and install it-Normally takes about 30 m if you have a good internet connection. If this doesn't work then take it to the apple store and they will guide you best if it can be repaired or not.
i also agree with Gio about the rice trick! however, it might be too late now, since your phone parts are already damaged.
Did you buy apple care with your iphone? Is it still covered under warranty- accidental one?
I wish you good luck!